SOLUTION: an amount is distributed equally among a certain no. of students.if there are 8 students less,everyone will get Rs.10 more. if there are 16 students more, each will get Rs.10 less
Question 619173: an amount is distributed equally among a certain no. of students.if there are 8 students less,everyone will get Rs.10 more. if there are 16 students more, each will get Rs.10 less. what is the no. of students and the amount each gets? what is the total amount distributed? Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! an amount is distributed equally among a certain no. of students.
if there are 8 students less, everyone will get Rs.10 more.
if there are 16 students more, each will get Rs.10 less.
what is the no. of students and the amount each gets?
what is the total amount distributed?
:
Let a = total amt
Let s = number of student
:
"If there are 8 students less, everyone will get Rs.10 more." - = 10
Multiply by s(s-8)
as - a(s-8) = 10s(s-8)
as - as + 8a = 10s^2 - 80s
8a = 10s^2 - 80s
:
"if there are 16 students more, each will get Rs.10 less." - = 10
Multiply by s(s+16)
a(s+16) - as = 10s(s+16)
as + 16a - as = 10s^2 + 160s
16a = 10s^2 + 160s
divide by 2
8a = 5s^2 + 80s
:
8a = 8a, therefore combine the two equations
10s^2 - 80s = 5s^2 + 80s
10s^2 - 5s^2 - 80s - 80s = 0
5s^2 - 160s = 0
Factor out s
5s - 160 = 0
5s = 160
s = 160/5
s = 32 students
:
Find the amt using 8a = 5s^2 + 80s, replace s with 32
8a = 5(32^2) + 80(32)
8a = 5120 + 2560
8a = 7680
a = 7680/8
a = $960 total distributed
:
Find the total for each student:
960/32 = $30 each student
:
:
:
Check this using the statement:
"If there were 8 less, each get $10 more
960/24 = $40, for each
:
You can check it in the other statement
